How your education policy is implemented is important.

It doesn't matter so much if the education system doesn't actively interact and get information on what the private sector needs. And creating a well functioning education system is very, very expensive. Basically you have to have that growing economy to support and sustain a great educational system.

Leaving it to charity won't work in my view. This is serious investment what we are talking about.

a university president or Nobel Laureate may be publicly chastised and even asked to resign for discussing hypotheses that are deemed politically incorrect. — NOS4A2

Hopefully you do understand the difference of a scientist getting attacked either because the scientific study he (or she) has made and/or the conclusions the scientist has made from the study and being attacked because publicly wearing a babe-shirt is offensive to some. There is a difference in the seriousness of the matter. Sticking to the trivial can be counterproductive.

this is important and not as dumb as you pretend. — NOS4A2

It's more important when actual scientific research is compromised or altered because of political correctness or political ideology, even if science has to deal with ethical questions. And there's a short distance from scientific ethics to political correctness or political ideology.

That might well be.

Yet when it comes to Trump, absolutely anything can happen between today and election day. One year and everything can look different. Who knows. The Trump Presidency hasn't been boring, so likely it won't be boring in 2020.

I'm just waiting when Jeffrey Epstein's surveillance tapes of both Bill Clinton and Donald Trump having sex with underage girls hits the fan. Never a boring day in Trumpland. :halo:

Talk about thread-drift. — John Gill

Exactly.

Perhaps it’s not high-brow enough for you. But I think that because it dumbs down public discourse is one of the reasons it should be opposed. I was only trying to give some examples. - What I’m trying to argue is that we should resist the pressure on science to conform to a limited, ever-changing and infantilizing lexicon of speech, in this case the lexicon of the politically correct. I’ve already given examples and shared the concurring arguments of others to give force to the argument. — NOS4A2

In my view comments about a shirt as an example of the effect of political correctness on science is itself dumbing down the issue. It's as far fetched as the tweets saying that the shirt shows how hostile STEM field is towards women.

Is this really about science? I don't think so. At least the picture meme below has partly the same narrative as NOS4A2 mentioned in


This is just a good example how stupid the debate becomes in social media. Hope PF doesn't go there.

Oh wait, we are there already.

The only question now is whether this maneuvering will more energize the left or the right in the upcoming election. It's doubtful it will change a single vote from one side to the next, but it might cause more people to go to the polls. — Hanover

This is the interesting question.

Who exactly will benefit from the upcoming impeachment ritual?

As noted by some people, in the end this might benefit Trump and just increase his status among his supporters as the "Teflon-President".

Yes. Cross party talks are bad. Far better to take the stance they have in the US: do not do anything with the administration if you are in opposition. If nothing works, that's good for you. :shade:

Honestly speaking there's a good path to follow here: be simply consistent on your agenda when talking to the administration. Don't flip flop here and there.

Seems like then you have your your own definition...

Definitons of axiom:

"An axiom is a proposition regarded as self-evidently true without proof. The word "axiom" is a slightly archaic synonym for postulate. Compare conjecture or hypothesis, both of which connote apparently true but not self-evident statements." Axiom - Wolfram Mathworld

"An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. " Axiom - Wikipedia

"1) a statement accepted as true as the basis for argument or inference. 2) an established rule or principle or a self-evident truth" axiom - Merriam Webster dictionary

You put 'axiom' in inverted commas for good reason, even if you didn't understand it. That all numbers are rational wasn't an axiom - it was a definition, an informal intuition, or a conjecture, depending on how they approached numbers in their thinking. — SophistiCat

Your reasoning of it being an conjecture or an informal intuition can be done only in hindsight. The definition of an axiom is "A self evident proposition requiring no formal demonstration to prove its truth, but received and assented
to as soon as mentioned". People were thinking about numbers and their commensurability exactly like as an axiom: a self evident proposition requiring no demonstration, something that was evident. Before it wasn't. And now it's an 'informal intuition'. Math simply is similar to science: we can make mistakes.

And I gave you an example where three different, consistent mathematics have been created based on three different axioms that contradict each other. The point is that neither mathematics, nor the axioms any specific field of mathematics is based on, are intended to represent absolute truth. You cannot win this debate with a nonsense claim like "the axiom is wrong." — JeffJo

Yet what you are stating is a philosophical view of mathematics. What you are basically saying is that: "You cannot win this debate because you don't accept formalism!"

Formalism goes exactly on these lines you said above: Math isn't a body of propositions representing an abstract sector of reality, but more akin to a game. Nothing to do with ontology of objects or properties and something more like chess. The truths expressed in logic and mathematics tell us hardly anything about numbers or sets themselves. It's just basically a game where axioms are just premises that define the system used and how useful the system is or isn't doesn't matter. Hence if you have a math system where 0=1, then it means just that anything goes, right? That's formalism.

And lastly, I'm not here to win anything, but to have a conversation from which I hopefully can learn something.

Education has been seen as this quasi-holy savior that solves nearly all problems in society.

Yet the fishing metaphor shows how naive the idea of education would be, if we would take it literally. The basic problem with the metaphor is that with it people sideline the true issue of a functioning economy with markets taking care of the supply and demand of labor. Charity isn't doing that. Charity is basically equivalent to central planning or an income transfer. Charity isn't at all even similar to a government program (of free education etc), a charity has to sell itself as a benign endeavor that people will give money to it and that people will feel happy afterwards.

So would it really make those otherwise starving to be fed if you teach them to fish? How do you teach them to fish? Do you teach them to angle? Do you give them a fishing rod and sent them wandering in the direction of a lake or the sea? This is what in figure of speech the worst aid programs are. Or do you make them fishermen capable of competing in the global market? So would your charity's objective be to teach them to operate a modern factory-at-sea fishing vessel and perhaps give them that vessel and send them to sail the seven seas to exploit those limited global fish reserves? Or would it more sustainable to teach them how to operate a fish farm? And how sustainable would a massive amount of fish farms be?

The classic idea of teaching Fishing - case 1:


The reality of Fishing. Really? This is the answer? - case 2:


Charities won't get money if they would help Third World countries with the slogan: "We'll transform the workforce of these poor countries to highly educated kick-ass competitive professionals so that global corporations will flock to move their factories to these countries from the US!"

With that slogan a charity won't get much money...at least in the US.


Better to make those BMW's in Africa!

My point is that they can't. That's why they are axioms. — JeffJo

I already gave an example of what was thought to be an axiom that wasn't. Greeks thought that all numbers were commensurable. The thought was for them self evident: math was so beautiful and harmonious. Yet all numbers weren't commensurable.There exists irrational numbers (and even transcendental numbers). What we had accepted to be true wasn't the case.

As Reuben Hersh says: "Mathematical knowledge isn’t infallible. Like science, mathematics can advance by making mistakes, correcting and recorrecting them."

Also a good point!

Avoided my ass.

Nope, what you are doing is this reurgitation of stories 'how out-of-whack and loony the PC crowd' is. What you are talking isn't even a media hype, but a typical twitter rant of some sort that pop up every now and then in social media. It really has absolutely nothing to do with science: so someone tweets that OMG! That lewd shirt means that women aren't welcome in the scientific community and some useless journalist who has nothing else up his or her sleeve tries to puff up this to something bigger... and then the anti-PC crowd notices it and takes it as an example how out of control the politically correct woke SJWs are today and so it goes on....

This is the dumbing down of public discourse that we see everywhere. When we treat something as bullshit as Twitter tweets as equivalent to Op-eds of serious media outlets (And I'm sure you'll find a genuine Op-ed about the lousy shirtgate), we get into this level of stupidity. It simply is counterproductive.

So let's have a serious discussion..... NOT!!! ROTFLMAO! :joke: :love: :snicker: :snicker: :snicker:

Really, NOS4A2, REALLY?

A lewd shirt??? That's your point?

Yeah, I know you started this thread... but this is the dumbing down of discourse. As some imbecile "shirtgate" would be about science.

Schäme dich!

Political correctness has been derided by pundits from all over the spectrum. — NOS4A2

Political correctness is used as a pejorative, yes. But it does also mean that language or policies are used with the intention to avoid offense or disadvantage to members of particular groups in society. Or then in a more general definition: something that is correct from a certain political viewpoint, but not universally accepted to be so.

1) If a scientific fact was politically explosive, would obscuring it be justified? (Could political correctness ever take precedence over scientific truth?)
2) Is there any specific instance of a scientific fact where this has taken place?

I would lean 'no' on the first one, but it's a very thorny issue. On 2) I believe the answer currently is 'no'.

So, what I would ask of you is can you find a specific instance where you can demonstrate the answer to 2) is 'yes' and do you have an unequivocal position on 1)? — Baden

Sure. I'll disagree with you on this matter and try to argue my point.

From history we find many examples of this, starting with Galileo Galilei, the Catholic Church and issues about how celestial bodies operate. The dilemma between Science and Religion is not only philosophical, but also quite political. Darwin's theories are still 'controversial' for some even today. This isn't limited just to science vs religion: when it is perceived that science clashes with our morals, people are up in arms about it. And sometimes it is very important to have the discussion on just what is morally correct and what isn't. If I remember correctly, Keith Campbell and Ian Wilmut, those scientists who made the first mammal clone with Dolly the Sheep, asked openly for a discussion and guideline on the topic.

We do not accept eugenics, the idea of excluding certain genetic groups judged to be inferior, but how do we in general approach genetic editing of humans? That we can engineer humans is that explosive scientific fact, a thing that we do might want to stop, which you asked about in question 1.

If in the future you don't use plastic surgery, but you genetically modify a human embryo (or the sperm and the ovula) that the human being becomes beautiful, athletic etc? What would happen when those that can afford buying genetic treatment that makes people healthier, smarter, stronger and/or better looking? Now it's still just science fiction, yet if we accept such treatment to fight hereditary or any other diseases, where do we draw the line? It is a political question.

The question isn't anymore theoretical after He Jiankui's experiments:

In November 2018, media from all over the world reported that two twin girls had been born with modified genes to make them HIV immune. Their birth was the result of an ‘experiment' (presently it can only be called that) conducted by He Jiankui with couples in which the males were HIV carriers. Using CRISPR technology to immunise the babies against the HIV virus, He Jiankui managed to disable the CCR5 gene that enables the HIV infection (although he still did not present complete evidence of this achievement).

The Chinese authorities suspended Jiankui's research and he has been fired from the University he worked in. So because of this, both questions 1 and 2 are in my view yes-answers.

My point is that science should remain ideology-free and scientists should have free reign to use the words they see fit. The threat from the religious is well-known and hardly warrants discussion, but the threat from the post-modernists and constructivists is becoming more apparent.

The Sokal affair is an example, but also the cancelling of Nobel Laureate Timothy Hunt proves pressure can result in loss of employment and social ostracism. — NOS4A2

The Sokal affair is more about lax scientific standards. He makes his argument even more clear in his book "Fashionable nonsense".

James Watson is one example of the minefield that a scientist gets into when he starts to talk about race. Hence the threat of ostracism is real.

The thing is that scientists cannot operate outside the society and scientists form a social group. That doesn't imply that using the scientific method you cannot get objective results, simply that we are prisoners of our time. The Kuhnian idea of Paradigms is correct in my view, but ought not to be given too much importance.

Can you have a look at what I said below. It seems wrong and right.
n(set of natural numbers) - n(set of even numbers) = infinity - infinity = zero because both are, well, infinite.
— TheMadFool

Consider two infinite sets A and B of equal cardinality i.e. n(A) = n(B) = infinity
Shouldn't n(A) - n(B) = 0?

Yet n(set of natural numbers, infinite) - n(set of even numbers, infinite) = n(set of odd numbers, infinite) which is infinite indicating that infinity - infinity = infinity — TheMadFool

Remember that Infinity is an endless series, not a number. Many would disagree with you if you treated infinity as a number! Some would say that infinity minus infinity is indeterminate. The following are considered to be indeterminate in form:



If you think that taking out the even numbers from the natural numbers you'll the odd numbers left, then you are thinking of a finite set. A finite set can not be in one-to-one correspondence with one of its proper subsets while an infinite one can be. Remember that you are talking about sets that are of INFINITE length. And because they are infinite, then you have the rule that part is as large as the whole: an infinite set is a set which is equivalent to a proper subset of itself.

1:23 Am here. I'll have to sleep on this. Take your time. :yawn:

I'll give you fifteen, old timer.

Such as... ? Where's the broad PC attack on science that we need to worry about going on? The only serious attacks on science I'm aware of are from the right. — Baden

I guess you didn't participate in the Decolonizing Science? thread. :wink:

Starting from taxonomic hierarchy, the rank below a subspecies is where the left goes all PC at an instant. Political correctness has made it that we avoid the whole term itself. Related to this is the age old question the role of genes versus learned traits, what is biological and what is social and learnt.

Then there's the leftist case against evolutionary psychology. If evolutionary psychology among other objectives looks to finding traits that have been shown to be universal in humans, it clashes head on to the question of what is universal for the species and what is dependent on cultural and particular historical circumstances.

And of course there is the assault against modifying plants and animals, even if we've been genetically modifying organisms for 10,000 years through breeding and selection.

Starting from the obvious examples of Lysenkoism, the left has as flagrantly as the (religious)right judged science based solely on political beliefs and ideology. Finally there's the whole dark pit of social sciences, which naturally are an open battleground for the left and the right. It's so bad that we make the separation between social sciences (and history) and the natural sciences.



Certain kind of science or scientists are typically erroneously thought to have an opposing political agenda, hence both left and the right attack that specific scientific research or scientists with equal vigor. And both leftist and right-wing politicians would be all too happy if they can argue their opinions by saying "It is a scientific fact!".

The value of a human being is the product of his labour; such has been the orthodoxy of economics, — unenlightened

I don't recall this from studying economics in the university. I thought the one they put on the pedestal was the consumer that optimizes his or her well being.

Or you just read only Marx or what?

Let's try to avoid making EVERYTHING a left vs right issue, NOS4A2.

And science IS politically neutral. Yes, they did it even in the Soviet Union as they did in liberal UK and US.

Anyway, even if the word "Quantum dominance" would trigger less foolishness, this is a typical nonsensical scaremongering to get more funds. The narrative is usually used in the China vs the US competition debate, where there is this outrageous claim that if China gets "Quantum Supremacy", they'll bury the US. That's why the term "supremacy".

I remember similar scares about Japan burying the US. And naturally the Soviet Union doing that with Sputnik.

Yes of course, but I don't know if you were aware, there is an equally pervasive issue with Islamophobia in the Tory party and opposition MPs repeatedly called this out, but it didn't cut through in the media and was repeatedly laughed off by Tory politicians. While the media couldn't stop talking about the media circus they had created around anti semitism in the Labour Party. — Punshhh

When you can laugh off things, things are good. But in the example I gave Blair wasn't laughing it off. And this was just one issue from many.

Here is the thing that is the problem of our time.

We assume that every political question divides by the juxtaposition of the left and right.

They simply don't, but the most vocal voices assume they do. Their argument creates the siren song of everything being part of a culture war and people being tribal. Yet Labour voter (and social democrats) and Conservatives in general simply don't fit such simplistic stereotype molds.

Just look at Brexit. A quarter of Leave-voters were supporters of Labour. Same is with any question on immigration, which was a major issue in the whole Brexit debate. Yes, I understood that you were talking about Islamophobia, but the general context of this debate is immigration policy. And it isn't as simplistic that the left is for open borders and the right is islamophobic or basically xenophobic nativists.

The worst thing is when we take some difficult area of environmental policy and then start to divide it along similar silly lines.

But there sure is a drive to dumb down the debate and cling to the most eccentric stereotypes that one can find on either side to show just how out of whack the other side is. The social media makes this so easy.

With all due respect, if you want "actual truth", then you do not understand the purpose of an axiom in mathematics. The point is that mathematics contains no concept of actual truth. — JeffJo

My point was that axioms can be possibly false. Our understanding can change. Best example of this was that until some Greeks found it not to be true, people earlier thought that all numbers are rational. Yet once when you prove there are irrational numbers, then the 'axiom' of all numbers being rational is shown not to be true.

And not all axioms are self evident. Just look at what Devans99 wrote about the axiom of infinity above

I think I get it now. The proper subset of the infinite set itself has to be infinite.The number of elements in a proper subset B of a finite set A is necessarily less than the number of elements in the set A. n(B) < n(A) so long as A and B are finite. - In other words the fact that the set of even numbers don't contain odd numbers and that the set of natural numbers is the union of odd and even numbers didn't translate into a numerical difference like it does with finite sets. — TheMadFool

Yep, you got it! :up:

This is btw. crucial to understand before the next step: comparing the natural numbers to the reals, which gets people really confused and asking a lot of questions. Just look at the thread Is Cantor wrong about more than one infinity.

Basically in infinite set the real question is can you get the numbers well ordered or not. Every non-empty well-ordered set has a least element. In layman terms, it's a question of can you list the numbers in the infinite set in such fashion that you can be sure to write every number. If you can do that, then the infinite set is of the same size as the natural numbers.

I think fishfry said something to the effect that bijection has precedence of injection. Why? — TheMadFool

I'm not sure what he meant, but a bijection is both an injection and a surjection.

But to your question: a set is infinite if and only if it is equivalent to one of its proper subsets. And this counters your argument. You are making the mistake of thinking about an infinite set as finite.

The proof of this actually refutes your idea: See for example here, Proof 1

You see with a finite set it isn't so: a finite set can not be in one-to-one correspondence with one of its proper subsets.

Ok, I'm listening, but the original point I was making that you replied to was about a long term (over a 100 year period) stream of anti socialism dogma. I wasn't really referring to recent developments, but rather that recent developments sit on the top of an edifice of anti socialist dogma and prejudice, Comy', Marxist, Trotskyist. They will let the Comy's in by the back door. — Punshhh

Well, there might be reason why especially from the historical point of view people would oppose socialism. It hasn't been all dancing on roses and happiness. In my family, two of my great grandfathers were nearly killed by the Red Guard during our War of Independence. They were defined to be the 'class enemy' by the dictatorship of the proletariat, hence the violent side of marxism (and especially Trotskyism) is something really true and not something that "just got understood the wrong way". And my grandfathers fought the Soviets in WW2. Back then the Workers Paradise was intent on annexing my little country. (The other grandfather was a surgeon, so he didn't literally fight).

I am aware of Blair's thoughts on this and accept that there is some anti-semitism in the Labour Party, but not as much as claimed by the media. The subtlety of the disitinction between "anti-Israeli foreign policy" sentiment and "anti-Israel" sentiment. Has been exploited by critics and sometimes mistakenly blurred by those being criticised. — Punshhh

But this is politics 1.0. It's basically quite arrogant not to understand how the other side will take your views. A mainstream party ought to look at what it says.

My beef in this is that I am anti-Brexit and Corbyn was our best hope in somehow stopping it. — Punshhh

I'm not sure if he was your best hope. I put my hope on politicians that take extremely seriously and treat with respect the people who oppose them and think differently. Far too often we just dismiss the opposing views and start to believe our own biased views.

Tbh when ever I see cries of ‘anti-semitism’ I assume they’re false. The reason being when I’ve looked further they are usually comments taken out of context and/or criticisms of the Israeli government. — I like sushi

Sure, but above with Blair you have a former leader of the Labour party saying: "The door was locked to those elements with a kind of 'not wellcome' sign on the door. And the truth is now because the leadership is from that tradition, the door is with a wellcome mat. And what's happened is you have had a whole lot of people come in to the Labour Party with these views" Later he says that singling out Israel "seeps into anti-semitism".

That's from a former leader of the party, a former prime minister. Not Labour's opponents.

The other thing is that the Brexit vote years ago didn't go by party lines. Roughly a quarter of the "Leave" vote was from voters that otherwise had voted for Labour.

Well the evidence is there in print, the bias and attack of any consideration of socialism by the right wing media. — Punshhh

Oh the right wing media...is (ghasp) against a labour candidate? And it's ugly?

Goodness Gracious! How terrible!!!

How could they?

The magazine Socialist Worker, the only populist left wing paper I know of was desolved in April this year. — Punshhh

And could you think of a reason for this? Or is it a huge conspiracy?

There is one left leaning mainstream newspaper The Gardian, but this paper gives politically balanced intellectual analysis of politics and is only left leaning by contrast to the right wing papers which predominate. It is widely regarded as having the highest standards of reporting in the UK. — Punshhh

But?

And what is the problem you have with the Guardian when you say "but this paper gives politically balanced intellectual analysis"? Is that really the problem? Perhaps you don't notice how condescending you come out with your remarks here. It is as if the (right wing) tabloid papers made distinct people not to vote Corbyn. Because...they are more stupid than you. They could be just lied to and that was it. Nothing else. That if (when) the other side, at least in your opinion, goes with propaganda, lies and fake news, is then the answer to have your own equivalent of propaganda, lies and fake news? Would you think that would be the answer? Or perhaps you mean that the Guardian isn't leftist at all. It just looks like it because of the contrast.

If it would be just the right wing tabloid press, basically the it would just backfire on them and create more support for labour, just like Trump bashing just makes Trump supporters love their "God Emperor" even more. Yet when you have the most successful labour politician of the past giving interviews like the one below, you cannot deny that there is a very serious problem. I cannot think of a more damning view coming from a previous prime minister of the party:



You might think high of Corbyn, you might think he's even too moderate. But the simple fact is labour voters, just as euro-social democrats they relate to, aren't in the far left. They are far more closer to the center than people may not think. This is because the most vocal people in parties don't actually reflect the majority of the party. Hence in a right wing party the loudest are far away on the right and in a leftist party the loudest are the those on the far left. The so-called purists.

, I would add that the drip feeding of anti socialism poison goes right back to the origin of the Labour Party and has become endemic now everywhere except for the metropolitan socialist elite and the younger educated voter. — Punshhh

Poison? The only poison has been fed to that metropolitan socialist elite and the younger 'educated' voter. It's their hubris, the idea that some of the previous supporters have been duped, that is the problem it. You have it totally the wrong way.

But by all means continue with it!

Still, the point here is nation-building, not fighting a landlocked war between Pakistani, Saudia Arabian, and Iranian influence. — Wallows

I think the structural problem is that if you go to war, your objective would be to win it. In truth, that hasn't been at all the objective. Nothing like that. Just fanciful rhetoric to pander the American voter. This is why American wars get so fucked up.

As the objective was to destroy a small cabal of terrorists and to do this a whole country was invaded and a regime that basically had nothing to do with the attacks apart from giving Bin Laden a refuge (just like Sudan had earlier given), the whole war was fucked up right from the start. This is because the occupation itself and the overthrow of the Taliban was the primary cause for the insurgency. It had nothing to do with the small Al Qaeda remnants that then did withdraw to Pakistan during the fighting. Yet if you remember at the time, Bush was not their to do nation building, but to fight Al Qaeda.

but wait, can a set be considered an element of itself??? — John Gill

If I remember correctly, some use that as a definition of infinity:

A set is infinite if and only if it is equivalent to one of its proper subsets.

Yeah well, it can happen that something that we have taken as an axiom isn't actually true.

Just look at how much debate here in this forum there is about infinity. Axiom of Infinity is anything but established and self-evidently true. The discussion here ought to show it. We just don't know yet! Bizarre to think that there are these gaping holes in our understanding of math, but they are there.

However, we still have to consider fact 2 by which we can determine inequality of cardinality of sets

The set of natural numbers N = {1, 2, 3, 4,...}

The set of even numbers E = {0, 2, 4, 6,...} — TheMadFool

No.

As we are talking of infinite sets, they aren't 'inequal'. They are indeed 'equal'.

You just take the set of N and multiply every number in N by two and presto! You have the set of even numbers.

It's the same if you would take the set of natural numbers and multiply every number with 1 000 000 and then the new set would be like Sn = ( 0, 1 000000, 2 000000, 3 000000, 4 000000,...) Now you would notice that there's a huge gap between the numbers, 999 999 numbers between every one. But this is simply the strange thing that you get with infinite sets. And basically again this is the Hilbert Hotel, which I remarked on the first page of this thread! (even if the picture seems not to be working)

It's clear that N can be separated into two proper subsets viz. the set of even numbers V = {0, 2, 4, 6,...} and the set of odd numbers, D = {1, 3, 5, 7,...}

Notice how set E has a bijection with set V and set V is a proper subset of set N. If so, then in accordance with fact 2 above, n(E) < n(N) i.e. the set of even numbers is less than the set of natural numbers.

This presents a problem doesn't it? — TheMadFool

Again no!

An infinite set is a set which is equivalent to a proper subset of itself. You can find the proofs online, similar as what I gave above.

What if he outright declares that the Mueller enquiry and the impeachment hearings really were a coup attempt and declares a state of emergency? — Wayfarer

Doesn't have to. Enough voters think it was so. Repetition is the way to get lies to work.

If you’re ever bored read through these Reddit threads. They are anecdotes of people who have worked for him or have met him. If what they say is true he it seems he is a very nice and likeable man, and not the villain people make him out to be. — NOS4A2

Yes, a guy who worked in a movie theatre that Trump visited is sorted to be the best answer.

Well, now we know how you make your opinion about him. :wink:

Yet how about making your opinion just listening what the man says and following what decisions he makes as President? The character issue is meaningless as we already know after many years what kind of President he is. Just a thought.

I think ‘Brexit’ is settled. (What an ugly neologism it has been, by the way.) It’s not done, but it’s decided — Wayfarer

Good riddance!

It is now nothing else but a distraction for the UK and a way to polarize the Brits.

What do you mean well ordered? Kindly explain. — TheMadFool

How about learning actual math? Set theory in this case. It's easy in our time. Just google it. I'll even give a link here: Well-order. Or here: Well ordered set or Well-ordering principle.

Or just watch the video short video:


Showing that you don't quite understand what others are talking about isn't a great argument.

And we don't prove existence. Axioms do. — JeffJo

I wouldn't agree on this. Axioms don't give proofs. Perhaps we are just thinking of this a bit differently.

A proof shows that something is true. If a mathematical object, a hypothesis, theorem, lemma is shown to be true, hence it is said to exist in the mathematical realm. It's hard to argue that something is illogical or false in math, if someone has given a logical proof for it. Axioms on the other hand are just given: "a statement or proposition which is regarded as being established, accepted, or self-evidently true." Or defined in a more mathematical way:

An axiom is a proposition regarded as self-evidently true without proof. The word "axiom" is a slightly archaic synonym for postulate. Compare conjecture or hypothesis, both of which connote apparently true but not self-evident statements.

Mathworld Wolfram

I have had a horrible thought about Trump - that the impeachment will turn out to be the Coronation of the Emperor. Meaning that, if/when the supine Senate Republicans absolve him of sin, then he has completely untrammelled reign, of the kind that he's behaved as if he's had since elected. I think if that happens we will begin to see the real Trump for the first time. — Wayfarer

Now this is great thinking from a fellow PF member, the reason why I participate in this Forum.

I totally agree with your view. The notion that Trump just springs back up after every put down will be seen as this positive sign of his abilities. The constant barrage of negative news about Trump will in the end help him. He is constantly repeating the mantra that everything, everything is a concentrated witch-hunt. It's a conspiracy against him. This actually is a winning formula. No matter how the facts wouldn't say that (like starting with Comey's October Surprise that made a devastating blow to Clintons campaign just before the election, that is totally forgotten in Trump's narrative). To repeat this mantra is simply soothing and makes people to close their ears. It's just the Trump derangement syndrome of the Trump haters. And when, I repeat when the GOP members of the Senate don't go with the impeachment, then Trump can truly say he has been vindicated, that it all was a witch-hunt. And republicans will do that. It will be the ticket for Trump to have a far better chance on winning again.

Global warming has been a hot topic of discussion for the last 40 years, conducted among smart, scientist-type adults. Did I hear about global warming in 1980? No. Back then, the burning issue was the ozone hole over the antarctic and diminished ozone in the upper atmosphere elsewhere. — Bitter Crank

Back then the whole thing was dealt differently. As you said, it indeed was a discussion conducted among smart, scientist-type adults. Now it's not.